We consider a model in which accelerated particles experience line-elements with maximal acceleration corrections that are introduced by means of successive approximations. It is shown that approximations higher than the first need not be considered. The method is then applied to the Kerr metric. The effective field experienced by accelerated test particles contains corrections that vanish in the limit h --> 0, but otherwise affect the behaviour of matter greatly. The corrections generate potential barriers that are external to the horizon and are impervious to classical particles. (C) 2001 Elsevier Science B.V. All rights reserved.